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A167347
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Totally multiplicative sequence with a(p) = (p-1)*(p-3) = p^2-4p+3 for prime p.
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1
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1, -1, 0, 1, 8, 0, 24, -1, 0, -8, 80, 0, 120, -24, 0, 1, 224, 0, 288, 8, 0, -80, 440, 0, 64, -120, 0, 24, 728, 0, 840, -1, 0, -224, 192, 0, 1224, -288, 0, -8, 1520, 0, 1680, 80, 0, -440, 2024, 0, 576, -64
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OFFSET
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1,5
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..1000
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FORMULA
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Multiplicative with a(p^e) = ((p-1)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)-3))^e(k). a(3k) = 0 for k >= 1, a(n) = A003958(n) * A166589(n).
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MATHEMATICA
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a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)
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CROSSREFS
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Sequence in context: A028636 A028620 A167300 * A028604 A292531 A337550
Adjacent sequences: A167344 A167345 A167346 * A167348 A167349 A167350
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KEYWORD
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sign,mult
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AUTHOR
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Jaroslav Krizek, Nov 01 2009
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STATUS
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approved
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